Question

One side of a right-angled triangle is f. The other two sides are 2 times bigger than f and 7 smaller than f. Write an expression for the perimeter of the triangle in its simplest form.

Answer 1

4f-7

Explanation:

You want the perimeter of a triangle whose side lengths are f, 2f, and f-7.

Perimeter

The perimeter is the sum of the side lengths:

P = f +2f +(f -7)

P = 4f -7

The perimeter of the triangle is 4f-7.

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Additional comment

No such triangle can exist. The sum of the two shortest sides is f+(f-7) = 2f-7, which is not greater than the longest side, 2f. The triangle inequality is not satisfied.